Monte Carlo methods for backward equations in nonlinear filtering
G. N. Milstein and M. V. Tretyakov
Source: Adv. in Appl. Probab. Volume 41, Number 1 (2009), 63-100.
Abstract
We consider Monte Carlo methods for the classical nonlinear filtering problem. The first method is based on a backward pathwise filtering equation and the second method is related to a backward linear stochastic partial differential equation. We study convergence of the proposed numerical algorithms. The considered methods have such advantages as a capability in principle to solve filtering problems of large dimensionality, reliable error control, and recurrency. Their efficiency is achieved due to the numerical procedures which use effective numerical schemes and variance reduction techniques. The results obtained are supported by numerical experiments.
Primary Subjects: 93E11, 65C30, 60G35, 60H35
Keywords: Pathwise filtering equation; stochastic partial differential equation; Monte Carlo technique; Kallianpur--Striebel formula; mean-square and weak numerical methods
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aap/1240319577
Digital Object Identifier: doi:10.1239/aap/1240319577
Zentralblatt MATH identifier:
1159.93359
Mathematical Reviews number (MathSciNet):
MR2514946
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